Hey guys, I was wondering if it would be possible for someone to check my work on a few calculus problems and, if they're wrong, to tell me what I'm doing wrong. Thank you very much in advance.
Problem 1. R is the region bounded by y = sinx and the lines x = 0 and x = .
a. Calculate the center of mass of the region R.
My Solution
dx
u = x, du = dx, dv = sinx dx, v = cosx
-xcosx + cosx dx = -xcosx + sinx
= = 1
dx = dx = dx = = = =
b. Use Pappus's Theorem to calculate the volume of the solid of revolution if R is revolved about the line x = 5.
My Solution
Area of region R = 1 (from problem 1a)
V = = =
c. Calculate the volume of the solid if R is revolved about the line y = -4.
My Solution
Area of region R = 1 (from problem 1a)
V = = =
Problem 2. Calculate each antiderivative.
a. dx
My Solution
x = , dx = d , =
= d = d = d = =
b. dx
My Solution
u = 1 - , du = -2x dx, dx = du
= du = du = du = =
c. dx
My Solution
, ,
= = d = d = = = = =
d. dx
My Solution
, ,
= = = = = = = = =
Once again, thank you very much in advance.
Thanks for the replies. Yeah it takes awhile to type up, but if people can't see my work they can't direct me to where I went wrong lol.
Now for 2c. I get and for problem 2d. I get . Are these solutions, along with the other problems I posted correct? Thanks in advance.